Nonlinear waves propagating over a conducting ideal fluid surface in an electric field

Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field

“…The study of the stability of interfacial electrohydrodynamic waves was initiated by Melcher [3] and Taylor and McEwan [13], and the role of interfacial stresses resulting from electrodes was reviewed by Melcher and Taylor [4]. Recent theoretical research in this field has focused on the nonlinear phenomena and corresponding mechanisms, such as nonlinear coherent structures (e.g., [2,5,8,10,11,[14][15][16][17][18][19][20]) and touchdown singularities (e.g., [7,21]). Considerable effects have been put into the modeling and numerical studies of nonlinear interfacial electrohydrodynamic waves.…”

“…On the numerical side, most researches focus on periodic waves (see, e.g., [5,7,10,14,21]); however the studies of electrified solitary waves have begun recently. Easwaran [23] first derived the Korteweg-de Vries (KdV) equation in the context of electrohydrodynamic waves which admits sech 2 soliton solutions naturally.…”

“…Recent study on 3D electrohydrodynamic modeling has focused on conducting fluids under normal electric fields: Hunt et al [18] proposed a one-way model with weak transverse variations which is called the Benjamin-Ono-Kadomtsev-Petviashvili equation, Aliev and Yurchenko [14] established a reduced system for the same setup, and Wang [8] developed fully nonlinear numerical models and weakly nonlinear theories for electrohydrodynamic surface waves in the Hamiltonian framework based on analyses of the Dirichlet-Neumann operators. In this paper, we are concerned with a dielectric liquid under a tangential electric field, and restoring forces due to gravity, surface tension, and Maxwell stresses are all taken into account.…”